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Find all right-angled triangles whose side lengths form an arithmetic sequence.

Correct answer:

n = ∞

Step-by-step explanation:

a2+b2=c2 b=a+Δ c=b+Δ = a + 2Δ  a2 + (a+Δ)2 = (a+2Δ)2 a2  2 a Δ  3 Δ2 = 0; a>0;  Δ>0 (a  3 Δ) (a + Δ) = 0; a>0;  Δ>0 a  3 Δ=0;  Δ>0 Δ = a/3  a = 33 x b = 34 x c = 35 x; x>0  n=   Verifying Solution:  a1=3 b1=34 a1=34 3=34 3=312=4 c1=35 a1=35 3=35 3=315=5  a2=5 b2=34 a2=34 5=34 5=3206.6667 c2=35 a2=35 5=35 5=3258.3333  a3=10 b3=34 a3=34 10=34 10=34013.3333 c3=35 a3=35 10=35 10=35016.6667  n=

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Showing 1 comment:
Dr Math
there are infinity solutions. for leg lenght a,  difference AP is a/3. So right triangle has sides: a, a+a/3, a+2/3a

So all triangles are similar to triangle 3-4-5 and has length of sides: a ; 4/3 a ; 5/3*a

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